In this book are gathered some studies about the mergers between Binary Neutron Stars and Neutron Star-Black Hole systems. In details are considered the Gravitational Waves (GWs), the short Gamma Ray Burst (sGRB) and the Kilonova emission from the mergers both from a theoretical approach and from the observation of the GW170817 event. It is also underlined the possibility of the discovery, from the analysis of the GW170817 event, of a new Compact Object which is the Quark Star.